$A$ box contains $8$ red and $7$ black balls. If two balls are drawn at random,the probability that both balls are of the same color is ...... .

From a month of $31$ days,$3$ different dates are selected at random. If the probability that these dates are in an increasing $A$.$P$. is equal to $\frac{a}{b}$,where $a, b \in N$ and $\text{gcd}(a, b) = 1$,then $a + b$ is equal to ————

$A$ container contains nine balls: three red,four blue,and two green. If three balls are selected at random from the container without replacement,what is the probability that all three balls are of different colors?

From a group of $50$ students,two sections comprising of $20$ and $30$ students are formed. If $Ram$ and $Rahim$ are two particular students among the $50$ students,then the probability that they both belong to the same section is

$A$ bag contains $4$ red and $4$ blue balls. Four balls are drawn one by one from the bag. Find the probability that the drawn balls are of alternating colors.

If the coefficients $a$ and $b$ of a quadratic expression $x^2+ax+b$ are chosen from the sets $A=\{3, 4, 5\}$ and $B=\{1, 2, 3, 4\}$ respectively,then the probability that the equation $x^2+ax+b=0$ has real roots is